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Abstract

We demonstrate polarization-selective microlensing and waveguiding of laser beams by birefringent profiles in bulk nematic fluids using numerical modelling. Specifically, we show that radial escaped nematic director profiles with negative birefringence focus and guide light with radial polarization, whereas the opposite – azimuthal – polarization passes through unaffected. A converging lens is realized in a nematic with negative birefringence, and a diverging lens in a positive birefringence material. Tuning of such single-liquid lenses by an external low-frequency electric field and by adjusting the profile and intensity of the beam itself is demonstrated, combining external control with intrinsic self-adaptive focusing. Escaped radial profiles of birefringence are shown to act as single-liquid waveguides with a single distinct eigenmode and low attenuation. Finally, this work is an approach towards creating liquid photonic elements for all-soft matter photonics.

Figures (6)

Fig. 1 Radial escaped nematic line as a photonic element. (A) An escaped profile of the nematic liquid crystal. Away from the axis, molecules are perpendicular to the escaped line, and continuously transition to a parallel orientation at the axis. (B) Radially polarized light (polarization illustrated by red arrows) propagating through a short segment of an escaped director profile observed a radially-dependent refractive index, resulting in focusing and lensing, while the polarization profile is preserved. The optical electric field Eopt, external electric field Eext, and the chosen coordinate system are shown with arrows.

Fig. 3 Lensing of high-intensity beams on an escaped disclination line in the presence of an external electric field. Shades of gray show the local light intensity with the scale given by colorbar under each image, red lines show the local director profile inside the liquid crystal lens, while green dashed lines mark the lens boundary. (A–I) Competition between elastic forces, optical fields of the beam with power P and an external electric field Eext produces a rich variety of lensing patterns. Interesting director structures form in medium-strength external fields (Eext ∼ 0.5 V/μm), where beam power P has a strong effect on the director profile and lensing. As the external field strength is increased, the structure transforms into a completely radial profile with a defect line at the axis. In all cases, light intensity is almost completely axially symmetric, as is the director angle of escape and with it the observed index of refraction.

Fig. 4 (A) Numerical aperture of the lens as a function of beam power in the absence of an external electric field. We see that the numerical aperture is highest for weak beams, then quickly drops as power is increased, and finally stabilizes at a lower value for high beam powers. The inset shows the director angle profiles at different beam powers. Strong beams reduce the director angle, resulting in a wide area where the director is parallel to the escaped line axis. (B) Director angle of escape at different external field strengths and a strong (P = 800 mW) light beam. When the external field is weak, below 0.5 V/μm, the director is mostly in the z direction. As the external field is increased, it gradually changes and the director becomes aligned in the xy plane. (C) The numerical aperture of the lens at different external field strengths and beam powers. The numerical aperture is highest at a distinct external field strength Eext, which depends on the beam power. Notably, changing the beam power shifts the position of this peak, demonstrating a possibility of tuning such lenses by varying either the beam power or the external field.

Fig. 5 Use of long escaped director profiles as waveguides. (A) Intensity profiles of incident beams of different widths show that the beams condense to the single eigenmode, which then remains stable for long distances. (B) Total beam power as a function of position inside the waveguide shows large initial losses, but confirms that the eigenmode is stable and the waveguide does not leak at larger distances. The magnitude of the losses depends on the incident beam width w0.

Fig. 6 (A) Cross-sections of the local light intensity show that the eigenmode is independent of the incident beam width w0. A Laguerre-Gaussian profile is fitted to the mode, which gives a beam width of w0 = 375 nm. Comparison to the Laguerre-Gaussian profile and the analytically obtained solution shows a discrepancy at the center, where simulation show nonzero intensity due to a presence of longitudinal polarization, while the analytic approaches assume zero intensity. (B) Spatial profile of the refractive index observed by the incident radially polarized beam and the stable waveguide mode. Discrepancies arise due to the presence of the longitudinal component at the center, as well as far away from the axis where the light intensity is very low.